Question

The coefficient of $a^8{b}^4{c}^9{d}^9$ in ${\left(abc+abd+acd+bcd\right)}^{10}$ is

• A. $10!$
• B. $\frac{10!}{8!4!9!9!}$
• C. 2520
• D. none of these

Answer 1

The correct option is C 2520

$(abc+abd+acd+bcd{)}^{10}$

then $a^8{b}^4{c}^9{d}^9=\left(abc{)}^l\right(abd{)}^m\left(acd{)}^n\right(bcd{)}^o$

$l+m+n=8$

$l+m+o=4$

$l+n+o=9$

$m+n+o=9$

On solving $l=1,m=1,n=6,o=2$

then coefficient of $a^3{b}^4{c}^9{d}^9=\frac{10!}{l!m!n!o!}$

$=\frac{10!}{1!6!1!2!}$

$=5\times 8\times 9\times 7$

$=2520$

$C$ is correct